Let us now highlight the important features that can be extracted from Fig. REF .
Each point in one of the six panels represents a choice of parameter values in the xSM.
That is, conventionally, one would draw an entire GW spectrum for each such point, which one would then have to compare to the standard power-law-integrated sensitivity curves (see Ref. [1]} for a more detailed discussion).
In our approach, by contrast, we simply need to verify whether a given point is above any of the six PISCs (of one experiment).
In that case, the SNR will automatically be larger than the predefined threshold (black points in Fig. REF ), indicating that this parameter point will be probed by LISA (or BBO, or DECIGO).
In the opposite case, the point may still surpass the SNR threshold, namely, if the sum of contributions is larger than the threshold.
We indicate such points by a dark gray color.
Finally, points that are not testable by LISA are shown in light gray.
This procedure allows us to map the phenomenologically relevant parameter space into the space of GW observables.
Note also that, for any contribution that depends on more than one peak frequency (i.e., the turbulence (t), sound wave / turbulence (s/t), and bubble collisions / turbulence (b/t) channels), we cannot draw a single PISC in a two-dimensional plot.
As a consequence, we draw peak-integrated sensitivity bands in these plots, where the peak frequency that is not shown is varied in a range that can either be chosen freely or according to the respective spread found in the data.The latter approach is to be preferred since it shrinks these bands to a minimally required width.
In Fig. REF , we indicate the intervals that we used for variation as they follow from the numerical data.
If we had not fixed the wall velocity at \(v_w = 0.9\) , we would also have to include a band in the bubble collisions / sound waves (b/s) channel; see Eq. ().
